COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > One-dimensional quasi-periodic Schrdinger operators III

## One-dimensional quasi-periodic Schrdinger operators IIIAdd to your list(s) Download to your calendar using vCal - Marx, C (Oberlin College)
- Thursday 15 January 2015, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Periodic and Ergodic Spectral Problems Quasi-periodic Schrdinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as “Hofstadter’s butterfly,” marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO , in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more “global,” model-independent point of view. Intriguing phenomena first encountered for the AMO , notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrdinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles’‘), which was successfully used to address several open problems (e.g. the ``Ten Martini problem’‘) and enabled above-mentioned global perspective. Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior – Anderson localization Subcritical behavior – Duality, reducibility, and absolutely continuous spectrum Avila’s global theory and critical behavior This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other lists2013 UK~IRC Innovation Summit Education, Equality and Development (EED) Group Seminars Type the title of a new list here## Other talksZone 6 Convention Computer vision techniques for measuring deformation Reframing African Studies through Languages and Translation: Overcoming Barricades to Knowledge and Knowledge Management MEMS Particulate Sensors Beacon Salon # 8 The Dawn of the Antibiotic Age Cooperation, Construction, Coercion, Consent: Understanding the Role of Reimagined Urban Space within Nazi Germany and Fascist Italy |